need a bit of help understanding exactly what this means

Question

Vocaloid · Answer

unifying fundamental theorem of vector integral calculus is defined as "the integral of a differential operator acting on a field over a region equals the sum of the field components appropriate to the operator over the boundary of the region"

@sillybilly123 would you mind putting this in layman's terms? my textbook doesn't really offer an explanation of this

sillybilly123 · Answer

That sounds impressive; but Stokes & Gauss, in my mind at least, work in different (not opposite) directions. Eg, Stokes requires a butterfly net, Gauss a closed volume. IMO, this is an interesting resource: https://mathinsight.org/fundamental_theorems_vector_calculus_summary Simplifying is great, the Gradient Theorem is also known as the Fundamental Theorem of Line Integrals. I think it was actually Heaviside that wrote much of Vector Calculus. Maxwell wrote scalar equations.

sillybilly123 · Answer

Hi.  Does that answer - I do not know !

Vocaloid · Answer

oh that's actually a really helpful link ty

sillybilly123 · Answer

Cool!  They create a potential function that is not conservative according to the usual tests you find in physic books.

Mathematicians :-(

Gn :-)